Before preparing the lobsters, chill them in the freezer 10 to 15 minutes. This has an anesthetizing effect on them.
Place 1 lobster, shell-side down (belly up), on a cutting board. Place the tip of a large knife in the center of the lobster, cut lobster in half from the center to the head, and then cut in half from the center to the tip of the tail. Pry open, leaving shell intact on back, if desired. Repeat with remaining lobster. Brush 1/3 cup Pesto on each lobster. Place lobsters on grill, shell-side up (belly down).
Grill, covered with grill lid, over medium-high heat 5 minutes on each side or until fully cooked. Remove from heat; baste with another 1/3 cup Pesto. Serve immediately.